# Exclusion Restriction Tests

**Reviewer Issue 3.1**: Demographic distance may proxy for migration,
trade, or technology diffusion channels.

## Test A: Trade Openness Control

| h | Baseline β | Baseline p | With trade β | With trade p |
|---|-----------|-----------|-------------|-------------|
| 0 | -1.6546*** | 0.0000 | -1.3540*** | 0.0000 |
| 1 | 0.1071 | 0.7314 | 0.1140 | 0.7171 |
| 2 | 0.6917** | 0.0437 | 0.6718* | 0.0515 |
| 3 | 0.2045 | 0.5539 | 0.2518 | 0.4677 |
| 4 | -0.3329 | 0.3336 | -0.3054 | 0.3764 |
| 5 | -0.5454 | 0.1129 | -0.5684 | 0.1000 |

Attenuation at h=2: 2.9% (baseline: 0.6917, with trade: 0.6718)

## Test B: Non-Financial Outcome Falsification

If the instrument affects these outcomes, the exclusion restriction is threatened.

| Outcome | h=0 | h=1 | h=2 | h=3 | h=4 | h=5 |
|---------|-----|-----|-----|-----|-----|-----|
| Δ(working-age share) | -0.0008*** | -0.0012*** | -0.0014*** | -0.0019*** | -0.0023*** | -0.0026*** |
| Δ(trade openness) | -0.6173 | 1.5554 | 1.4083 | 1.2581 | -3.9009*** | -5.0372*** |
| Δlog(employment) | -0.0066*** | 0.0028 | 0.0148*** | 0.0152*** | 0.0103** | 0.0075 |

## Test C: Remittance Control

| h | With remittance β | p |
|---|------------------|---|
| 0 | -1.6408*** | 0.0000 |
| 1 | 0.1296 | 0.6761 |
| 2 | 0.7065** | 0.0392 |
| 3 | 0.1994 | 0.5633 |
| 4 | -0.3123 | 0.3645 |
| 5 | -0.5208 | 0.1295 |

## ASCII IRF Plots

```
Baseline (no trade control)
===========================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
  0   -1.65463***  0.30187 0.0000    703  ---------*----------                |                       
  1       0.10712  0.31194 0.7314    703                              ----------·----------           
  2     0.69170**  0.34238 0.0437    703                                      |-----------*-----------
  3       0.20450  0.34535 0.5539    703                              ------------·-----------        
  4      -0.33285  0.34401 0.3336    703                      -----------·-----------                 
  5      -0.54542  0.34358 0.1129    703                  -----------·-----------                     
                                          ------------------------------------------------------------
        -2.2463                                            1.3628
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

With trade_openness control
===========================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
  0   -1.35395***  0.29768 0.0000    703  ----------*----------             |                         
  1       0.11399  0.31448 0.7171    703                           -----------·-----------            
  2      0.67175*  0.34432 0.0515    703                                    ------------o-------------
  3       0.25175  0.34650 0.4677    703                             ------------·------------        
  4      -0.30538  0.34500 0.3764    703                   ------------·------------                  
  5      -0.56838  0.34512 0.1000    703              ------------·------------                       
                                          ------------------------------------------------------------
        -1.9374                                            1.3466
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

Falsification: demo_inflows → Δ(working-age share)
==================================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
  0   -0.00078***  0.00018 0.0000    703                                          ------*-----       |
  1   -0.00121***  0.00026 0.0000    703                                --------*---------           |
  2   -0.00139***  0.00033 0.0000    703                           ----------*-----------            |
  3   -0.00193***  0.00039 0.0000    703                ------------*-------------                   |
  4   -0.00232***  0.00044 0.0000    703       ---------------*--------------                        |
  5   -0.00258***  0.00049 0.0000    703  ----------------*----------------                          |
                                          ------------------------------------------------------------
        -0.0035                                            0.0000
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

Falsification: demo_inflows → Δ(trade openness)
===============================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
  0      -0.61728  0.47986 0.1987    703                                 -----·-----                  
  1       1.55544  0.94811 0.1013    703                                        ---------·----------  
  2       1.40827  1.10313 0.2022    703                                     ------------·----------- 
  3       1.25807  1.24532 0.3127    703                                   -------------·-------------
  4   -3.90086***  1.30263 0.0028    703        -------------*-------------      |                    
  5   -5.03721***  1.36923 0.0003    703  -------------*--------------           |                    
                                          ------------------------------------------------------------
        -7.7209                                            3.6989
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

Falsification: demo_inflows → Δlog(employment)
==============================================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
  0   -0.00665***  0.00187 0.0004    703  ------*------    |                                          
  1       0.00280  0.00327 0.3921    666             -----------·-----------                          
  2    0.01478***  0.00413 0.0004    629                   |          --------------*--------------   
  3    0.01520***  0.00466 0.0012    592                   |         ----------------*----------------
  4     0.01031**  0.00494 0.0375    555                   |-----------------*----------------        
  5       0.00753  0.00527 0.1535    518              ------------------·-----------------            
                                          ------------------------------------------------------------
        -0.0103                                            0.0243
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

With remittance control
=======================

  h          coef       SE      p      N  Plot
  -          ----       --    ---    ---  ------------------------------------------------------------
  0   -1.64080***  0.30001 0.0000    699  ---------*----------                |                       
  1       0.12958  0.30998 0.6761    699                              ----------·----------           
  2     0.70653**  0.34199 0.0392    699                                      |-----------*-----------
  3       0.19940  0.34484 0.5633    699                              -----------·-----------         
  4      -0.31232  0.34420 0.3645    699                      -----------·-----------                 
  5      -0.52078  0.34309 0.1295    699                  -----------·-----------                     
                                          ------------------------------------------------------------
        -2.2288                                            1.3768
  (* p<0.05, o p<0.1, · p>0.1, | = zero)

```
